Work

Characters, Hall subgroups, and Normal Complements

Year: 2024

Type: preprint

Abstract: If $H$ is a Hall subgroup of a finite group $G$, it was proven in 1989 using the classification of finite simple groups that all the irreducible complex characters of $H$ extend to $G$ if and only if there is $N\trianglelefteq G$ such that $HN=G$ and $H\cap N=1$. In this note we offer a modular version of this result under more general hypothesis.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2406.16184

Authors: Guralnick, Robert, Navarro, Gabriel

Institutions: University of Southern California, Universitat de València

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, European Regional Development Fund, Agencia Estatal de Investigación

Awards: G1175115578, G2262748287, Cohomology and Representations of Finite and Algebraic Groups with Applications, G300979063, G34346518, G3480869486, G410571670, G425668148, G451917667, G5080475149, G5967599077, G6507757115, G7001747737

OpenAlex ID: W4400023587

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